# The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

## Solution :

Let the number of boys and girls be x and y, respectively

$$\therefore$$   52x + 42y = 50(x + y)

$$\implies$$  52x + 42y = 50x + 50y

$$\implies$$  2x = 8y

$$\implies$$  x = 4y

$$\therefore$$  Total number of students in the class

= x + y = 4y + y = 5y

$$\therefore$$  Required number of boys

= $$4y\over 5y$$ $$\times$$ 100% = 80%

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